The invention relates to an air flow rate meter for use in the fuel supply system of a mixture compressing externally ignited internal combustion engine. The air flow rate meter is disposed movably within the induction tube of the engine and is subject to a restoring force. Its displacement becomes a measure of the aspirated air quantity. In known fuel injection systems of this general type, the air quantity flowing through the induction tube is measured by an air flow rate meter and fuel is metered out proportional to the air quantity separately for each engine cylinder and is injected separately by individual injection valves in the vicinity of each cylinder. In such a construction, the lateral surfaces of the air flow element cooperate with the induction tube walls to provide a sealing function which prevents air flow in between the two surfaces into the induction tube region downstream of the flow meter. Such a leakage air flow would alter the downstream pressure and would result in an erroneous indication by the air flow rate meter. However, the clearance between the cooperating surfaces cannot be made arbitrarily small because vibrations and temperature changes, for example, could result in dimensional changes that would affect the operational reliability if the clearance between the two surfaces were too small. A fuel injection device is already known, in which the air flow rate meter is arranged in the air induction tube downstream of the butterfly valve. This arrangement has the disadvantage, that the changing air density downstream of the butterfly valve causes an undesirable change of the fuel-air mixture.